The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space with respect to their frequencies, amplitudes and phase angles. In this article, we present several theoretical and practical aspects of measuring Fourier rheology spectra with high sensitivity. Using the hardware of a conventional rheometer, Fourier rheology spectra with a signal-to-noise ratio of about 18,000:1 for a single acquisition were obtained. This allowed the observation of harmonics up to the 21st harmonic. Signal averaging can further increase the sensitivity.